One-particle Spectral Function Research Articles

Pair-fluctuation-induced pseudogap in the normal phase of the two-dimensional attractive Hubbard model at weak coupling

One-particle spectral properties in the normal phase of the two-dimensional attractive Hubbard model are investigated in the weak-coupling regime using the non-self-consistent T-matrix approximation. The corresponding equations are evaluated numerically directly on the real-frequency axis. For temperatures sufficiently close to the superconducting transition temperature, a pseudogap in the one-particle spectral function is observed, which can be assigned to the increasing importance of pair fluctuations.

Some sum rules for non-Fermi liquids: Applications taking into account the mass renormalization factor

Re-studying the non-fermi liquid one-particle Green function (NFLGF) we have extended the work of A. Balatsky (Phil. Mag. Lett. 68, 251 (1993)) and L. Yin and S. Chakravarty (Int. J. Mod. Phys. B 10, 805 (1996)), among others. We used the moment approach of W. Nolting (Z. Phys. 255, 25 (1972)) to compute the unknown parameters of the NFLGF's in the framework of the Hubbard model. The zeroth order momentum requires that our one-particle Green function describe fermionic degrees of freedom. In order to satisfy the first order sum rule a renormalization, $\gamma\neq 1$, of the free electron mass is called for. The second order sum rule or moment imposes a relation between the non-Fermi liquid parameter, $\alpha$, the Coulomb interaction, U, and the frequency cutoff, $\omega_c$. We have calculated the effect of the mass renormalization factor, $\gamma$, on some physical quantities. As a new class of non-Fermi liquid systems, in Appendix A, we have studied two inequivalent coupled Hubbard layers for which we calculated the one-particle spectral functions on the layers and perpendicular to them. We discuss the new features which appear due to the shift in the two effective chemical potentials and proposed some experiments to detect the features founded from our expressions.

Correlation Effects on the Double Exchange Model in a Ferromagnetic Metallic Phase

The effect of the Hubbard interaction among conduction electrons on the double exchange model is investigated in a ferromagnetic metallic phase. Applying iterative perturbation theory to the Hubbard interaction within dynamical mean field theory, we calculate the one-particle spectral function and the optical conductivity, in which coherent-potential approximation is further used to treat the ferromagnetic Hund coupling between conduction electrons and localized spins. Identifying the decrease of the magnetization for the localized spin with the increase of the temperature, we discuss the temperature dependence of the one-particle spectrum and the optical conductivity. It is found that the interplay between the Hund coupling and the Hubbard interaction dramatically changes the spectral function, while it is somehow obscured in the optical conductivity.

Relationship between spiral and ferromagnetic states in the Hubbard model in the thermodynamic limit

We explore how the spiral spin (SP) state, a spin singlet known to accompany fully polarized ferromagnetic (F) states in the Hubbard model, is related with the F state in the thermodynamic limit using the density-matrix renormalization group and exact diagonalization. We first obtain an indication that when the F state is the ground state the SP state is also eligible as the ground state in that limit. We then follow the general argument by Koma and Tasaki [J. Stat. Phys. 76, 745 (1994)] to find that (i) the SP state possesses a kind of order parameter, and (ii) although the SP state does not break the SU(2) symmetry in finite systems, it does so in the thermodynamic limit by making a linear combination with other states that are degenerate in that limit. We also calculate the one-particle spectral function and dynamical spin and charge susceptibilities for various one-dimensional finite-size lattices. We find that the excitation spectra of the SP state and the F state are almost identical. The present results suggest that the SP and the F states are equivalent in the thermodynamic limit. These properties may be exploited to determine the magnetic phase diagram from finite-size studies.

One-Particle Spectral Properties of 1D Mott-Hubbard Insulators

We use an exact {\it holon} and {\it spinon} Landau-liquid functional which describes the holon - spinon interactions at all scattering orders, to study correlation functions of integrable multicomponent many-particle problems showing both linear and non-linear energy bands. Motivated by recent photoemission experiments, we consider specific cases when the dominant non-linear band terms are quadratic and apply our results to the evaluation of the half-filling 1D Hubbard model one-particle spectral functions beyond conformal-field theory.

Pseudogap formation in an electronic system withd-wave attraction at low density

On the basis of an electronic model with separable attractive interaction, the precursors at high temperature and strong coupling of the d-wave superconducting state are investigated in the one-particle spectral function $A(\mathbf{k},\ensuremath{\omega})$ and the total density of states $\ensuremath{\rho}(\ensuremath{\omega}),$ with the use of the self-consistent t-matrix approximation. In the low-density region, it is found that a gaplike structure at the Fermi level appears in $A(\mathbf{k},\ensuremath{\omega})$ and $\ensuremath{\rho}(\ensuremath{\omega})$ above the superconducting transition temperature. It is shown that the pseudogap energy scale is determined by the binding energy of the Cooper pair.

Pseudogap Formation in Models for Manganites

The density of states and one-particle spectral function $A(\mathbf{k},\ensuremath{\omega})$ of the one- and two-orbital models for manganites, the latter with Jahn-Teller phonons, are evaluated using Monte Carlo techniques. Unexpectedly robust pseudogap (PG) features were found at low and intermediate temperatures, particularly at or near regimes where phase separation occurs as $T\ensuremath{\rightarrow}0$. The PG follows the chemical potential and is caused by the formation of ferromagnetic metallic clusters in an insulating background. It is argued that PG formation should be generic of mixed-phase regimes. The results are in good agreement with recent photoemission experiments for ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$.

Hole-density evolution of the one-particle spectral function in doped ladders

The spectral function $A({\bf q}, \omega)$ of doped $t-J$ ladders is presented on clusters with up to $2 \times 20$ sites at zero temperature applying a recently developed technique that uses up to $\sim 6 \times 10^6$ rung-basis states. Similarities with photoemission results for the 2D cuprates are observed, such as the existence of a gap at $(\pi,0)$ near half-filling (caused by hole pair formation) and flat bands in its vicinity. These features should be observable in ARPES experiments on ladders. The main result of the paper is the nontrivial evolution of the spectral function from a narrow band at $x=0$, to a quasi-noninteracting band at $x \geq 0.5$. It was also observed that the low-energy peaks of a cluster spectra acquire finite line-widths as their energies move away from the chemical potential.

Excitation spectrum of the two-dimensional attractive Hubbard model

We calculate the one-particle spectral functions above the superconducting transition temperature T C, in the framework of a functional integral approach. The coupling of the electronic self-energy to pair fluctuations, which are treated by means of a time-dependent Ginzburg–Landau equation, yields a double-peak structure, around the Fermi wavenumber. The peak separation is essentially temperature-independent, but the structure sharpens when T C is approached.

STRONG COUPLING APPROACH TO ONE-DIMENSIONAL HUBBARD MODEL AND RELATED LATTICE MODELS

The strong coupling limit of one-dimensional correlated systems is nontrivial, but simple in some sense. Here we demonstrate it, discussing the wave functions for the 1D U→ +∞ Hubbard model, which are factorized as a direct product of the charge part and the spin part and determining the one-particle spectral functions explicitly.

Finite Temperature Effects in a One-Dimensional Mott-Hubbard Insulator: Angle-Resolved Photoemission Study ofNa0.96V2O5

We have made an angle-resolved photoemission study of a one-dimensional Mott-Hubbard insulator ${\mathrm{Na}}_{0.96}{\mathrm{V}}_{2}{\mathrm{O}}_{5}$ and found that the spectra of the V $3d$ lower Hubbard band are strongly dependent on the temperature. We have calculated the one-particle spectral function of the one-dimensional $t\ensuremath{-}J$ model at finite temperatures by exact diagonalization and compared them with the experimental results. Good overall agreement is obtained between experiment and theory. The strong finite temperature effects are discussed in terms of the existence of the ``Fermi surface'' of the spinon band.

Photoemission, inverse photoemission and superconducting correlations in Hubbard and t-J ladders: role of the anisotropy between legs and rungs

Several experiments in the context of ladder materials have recently shown that the study of simple models of anisotropic ladders (i.e. with different couplings along legs and rungs) is important for the understanding of these compounds. In this paper Exact Diagonalization studies of the one-band Hubbard and t-J models are reported for a variety of densities, couplings, and anisotropy ratios. The emphasis is given to the one-particle spectral function A(q,\omega) which presents a flat quasiparticle dispersion at the chemical potential in some region of parameter space. This is correlated with the existence of strong pairing fluctuations, which themselves are correlated with an enhancement of the bulk-extrapolated value for the two-hole binding energy as well as with the strength of the spin-gap in the hole-doped system. Part of the results for the spectral function are explained using a simple analytical picture valid when the hopping along the legs is small. In particular, this picture predicts an insulating state at quarter filling in agreement with the metal-insulator transition observed at this special filling for increasing rung couplings. The results are compared against previous literature, and in addition pair-pair correlations using extended operators are also here reported.

MATRIX ELEMENT EFFECTS IN THE ANGLE-RESOLVED PHOTOEMISSION SPECTRUM OF BISCO

We report first-principles angle-resolved photointensity (ARPES) simulations in Bi2212 in order to assess the importance of matrix element effects in the ARPES spectra. Our calculations properly account for the photoemission process and include full crystal wavefunctions of the initial and final states in the presence of the surface. The spectral weight of the ARPES feature associated with the CuO 2 plane bands is found to be strongly anisotropic in the ( k x , k y ) plane. These results indicate that the relationship between the ARPES intensities and the underlying electronic structure can be quite complicated and that caution should be exercised in interpreting detailed features of the ARPES intensities in terms of the properties of the theoretical one-particle spectral density functions.

Superconducting properties of the attractive Hubbard model

A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities.

Exact Results for Highly Correlated Electron Systems in One Dimension

One-dimensional conductors are a long-standing topic of research with direct applications to organic conductors and mesoscopic rings. The discovery of the ceramic high-temperature superconductors has revitalized the interest in low-dimensional charge and spin fluctuations of highly correlated electron systems. Several mechanisms proposed to explain the high-T c superconductors invoke properties of the two-dimensional Hubbard model, but probably also some one-dimensional aspects are relevant. Numerous one-dimensional models for correlated electrons have been studied with various approximate, asymptotically exact and exact methods. These results lead to the concept of Luttinger liquid for interacting electron gases without excitation gaps (metallic systems). Characteristic of Luttinger liquids are the charge and spin separation, marginal Fermi liquid properties, e.g. the absence of quasiparticles in the vicinity of the Fermi surface, nonuniversal power-law singularities in the one-particle spectral function and the related absence of a discontinuity in the momentum distribution at the Fermi level, the power-law decay of correlation functions for long times and large distances, persistent currents in finite rings, etc. Due to the peculiarities of the phase space in one dimension some of the models have sufficient conserved currents to be completely integrable. We review exact results derived within the framework of Bethe's ansatz for integrable one-dimensional models of correlated electrons. The Bethe-ansatz method is presented by explicitly showing the steps leading to the solution of the N-component electron gas interacting via a δ-function potential (repulsive and attractive interaction), which is probably the simplest model of correlated electrons. Emphasis is given to the procedure to extract the groundstate properties, the classification of states, the excitation spectrum, the thermodynamics and finite size effects, such as critical exponents of correlation functions and persistent currents. The method is then applied to numerous other models, e.g. (i) a two-band model involving attractive and repulsive potentials and crystalline fields splitting the bands, (ii) the traditional Hubbard chain with attractive and repulsive U, (iii) the degenerate Hubbard model with repulsive U, which displays a metal–insulator transition at a finite U, (iv) a two-band Hubbard model with repulsive U, (v) the traditional supersymmetric t–J model (vi) a two-band supersymmetric t–J model with band-splitting and (vii) the N-component supersymmetric t–J model. Finally, results for models with long-range interactions, in particular r-2 and sinh -2(r) potentials, are briefly reviewed.

Anomalous superconductivity in the tJ model: moment approach

By extending the moment approach of Nolting (Z. Phys. 225 (1972) 25) in the superconducting phase, we have constructed the one-particle spectral functions (diagonal and off-diagonal) for the tJ model in any dimensions. We propose that both the diagonal and the off-diagonal spectral functions are composed of two peaks. This ansatz satisfies the sum rules for the first four moments of the spectral functions. Our solutions are valid for J/ t ≤ 2.0. Our set of non-linear equations has been solved self-consistently. We obtain, in addition to the classical Hartree shift, a second Hartree shift which in the end result enlarges the bandwidth of the free carriers allowing us to take relative high values of J/ t and allowing superconductivity to live in the T c− ϱ phase diagram, in agreement with numerical calculations in a cluster. We have calculated the static spin susceptibility, χ( T), and the specific heat, C υ( T) , within the moment approach. We find that all the relevant physical quantities show the signature of superconductivity at T c in the form of kinks (anomalous behavior or jumps, for low density, in agreement with recent published literature, showing a generic behavior (model independence). We briefly indicate how to include correlations in the moment approach.

Moment approach for the 2D attractive Hubbard model

We constructed the one-particle spectral functions (diagonal and off-diagonal) which reproduce BCS for weak coupling and which take into account the effect of correlations on superconductivity in the attractive Hubbard model. The diagonal spectral function is composed of three peaks and the off-diagonal one is composed of two peaks. This ansatz satisfies the sum rules for the first six moments. Our solutions are valid for intermediate coupling, i.e., for U/ t ≈ −4.0. Our set of analytical equations for the unknown variables is self-consistent and has been solved numerically in lowest order of the order parameter. As a result, we obtain that the presence of the third band, or upper Hubbard band, strongly renormalizes the two lower bands, making that the energy gap be k-dependent while the order parameter is pure s-wave. This shows that the order parameter and the gap are two different quantities.

Dynamical properties of two coupled Hubbard chains at half-filling.

Using grand canonical Quantum Monte Carlo (QMC) simulations combined with Maximum Entropy analytic continuation, as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at half-filling. The one-particle spectral weight function, $A({\bf k},\omega)$, undergoes a qualitative change with interchain hopping $t_\perp$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large $t_\perp$. For smaller $t_\perp$, $A({\bf k}, \omega)$ is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange $J$ reasonably well-described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral $t$, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large $t_\perp$ and to the results of spin-wave theory for small $t_\perp$.

Excitation spectrum of the attractive Hubbard model.

We study excitation-spectrum and normal-state properties of the two-dimensional attractive Hubbard model using the conserving, self-consistent {ital T}-matrix formalism in the intermediate coupling regime and at low electron concentration. Numerical results are presented for one-particle and two-particle excitation spectra, the one-particle momentum distribution, the chemical potential, and the static spin susceptibility. For a coupling strength of {ital U}/{ital t}=4.0, the one-particle spectral function, {ital A}(k,{omega}), shows two peaks of different weights. One peak can be associated with pair formation, whereas the other corresponds to renormalized quasiparticle excitation. It turns out that the two-band feature is reasonably well described by an ansatz for {ital A}(k,{omega}), which satisfies the first four frequency moments.

Spectral function of the 1D Hubbard model in the U-->+

We show that the one-particle spectral functions of the one-dimensional Hubbard model diverge at the Fermi energy like $|\omega-\varepsilon_F|^{-3/8}$ in the $U\to +\infty $ limit. The Luttinger liquid behaviour $|\omega-\varepsilon_F|^\alpha$, where $\alpha \to 1/8$ as $U\to +\infty $, should be limited to $|\omega-\varepsilon_F| \sim t^2/U$ (for $U$ large but finite), which shrinks to a single point, $\omega=\varepsilon_F$,in that limit. The consequences for the observation of the Luttinger liquid behaviour in photoemission and inverse photoemission experiments are discussed.